scholarly journals The maximum size of a partial spread II: Upper bounds

2017 ◽  
Vol 340 (7) ◽  
pp. 1481-1487 ◽  
Author(s):  
Esmeralda Năstase ◽  
Papa Sissokho
Keyword(s):  
Maximum Size ◽  
Upper Bounds ◽  
Partial Spread

scholarly journals Improved Bounds on mr(2,q) q=19,25,27

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Rumen Daskalov ◽  
Elena Metodieva
Keyword(s):  
Projective Plane ◽  
Maximum Size ◽  
Upper Bounds ◽  
Computer Search ◽  
Lower And Upper Bounds ◽  
Local Computer

An (n,r)-arc is a set of n points of a projective plane such that some r, but no r+1 of them, are collinear. The maximum size of an (n,r)-arc in PG(2, q) is denoted by mr(2, q). In this paper, a new (286, 16)-arc in PG(2,19), a new (341, 15)-arc, and a (388, 17)-arc in PG(2,25) are constructed, as well as a (394, 16)-arc, a (501, 20)-arc, and a (532, 21)-arc in PG(2,27). Tables with lower and upper bounds on mr(2, 25) and mr(2, 27) are presented as well. The results are obtained by nonexhaustive local computer search.

scholarly journals The maximum size of a partial spread in H(5,q2) is q3+1

2007 ◽  
Vol 114 (4) ◽  
pp. 761-768 ◽  
Author(s):  
J. De Beule ◽  
K. Metsch
Keyword(s):  
Maximum Size ◽  
Partial Spread

scholarly journals The Maximum Size of a Partial Spread in $H(4 n +1, q^2)$ is $q^{2 n +1}+1$

10.37236/251 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Frédéric Vanhove
Keyword(s):  
Maximum Size ◽  
Polar Space ◽  
Maximal Dimension ◽  
Partial Spread ◽  
Isotropic Subspaces ◽  
Hermitian Polar Space ◽  
Totally Isotropic Subspaces

We prove that in every finite Hermitian polar space of odd dimension and even maximal dimension $\rho$ of the totally isotropic subspaces, a partial spread has size at most $q^{\rho+1}+1$, where $GF(q^2)$ is the defining field. This bound is tight and is a generalisation of the result of De Beule and Metsch for the case $\rho=2$.

scholarly journals Constant Rank-Distance Sets of Hermitian Matrices and Partial Spreads in Hermitian Polar Spaces

10.37236/3534 ◽  
2014 ◽  
Vol 21 (1) ◽  
Author(s):  
Rod Gow ◽  
Michel Lavrauw ◽  
John Sheekey ◽  
Frédéric Vanhove
Keyword(s):  
Maximum Size ◽  
General Notion ◽  
Partial Spread ◽  
Constant Rank ◽  
Hermitian Matrices ◽  
Rank Distance ◽  
Partial Spreads ◽  
Related Notion ◽  
Distance Set ◽  
Distance Sets

In this paper we investigate partial spreads of $H(2n-1,q^2)$ through the related notion of partial spread sets of hermitian matrices, and the more general notion of constant rank-distance sets. We prove a tight upper bound on the maximum size of a linear constant rank-distance set of hermitian matrices over finite fields, and as a consequence prove the maximality of extensions of symplectic semifield spreads as partial spreads of $H(2n-1,q^2)$. We prove upper bounds for constant rank-distance sets for even rank, construct large examples of these, and construct maximal partial spreads of $H(3,q^2)$ for a range of sizes.

scholarly journals Cross-Intersecting Erdős-Ko-Rado Sets in Finite Classical Polar Spaces

10.37236/4734 ◽  
2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Ferdinand Ihringer
Keyword(s):  
Maximum Size ◽  
Upper Bounds ◽  
Polar Space ◽  
Polar Spaces ◽  
The Cross ◽  
Classical Polar Spaces

A cross-intersecting Erdős-Ko-Rado set of generators of a finite classical polar space is a pair $(Y, Z)$ of sets of generators such that all $y \in Y$ and $z \in Z$ intersect in at least a point. We provide upper bounds on $|Y| \cdot |Z|$ and classify the cross-intersecting Erdős-Ko-Rado sets of maximum size with respect to $|Y| \cdot |Z|$ for all polar spaces except some Hermitian polar spaces.

scholarly journals Induced and Non-induced Forbidden Subposet Problems

10.37236/4644 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Balázs Patkós
Keyword(s):  
Asymptotic Behavior ◽  
Boolean Lattice ◽  
Maximum Size ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Extra Condition ◽  
Multi Level

The problem of determining the maximum size $La(n,P)$ that a $P$-free subposet of the Boolean lattice $B_n$ can have, attracted the attention of many researchers, but little is known about the induced version of these problems. In this paper we determine the asymptotic behavior of $La^*(n,P)$, the maximum size that an induced $P$-free subposet of the Boolean lattice $B_n$ can have for the case when $P$ is the complete two-level poset $K_{r,t}$ or the complete multi-level poset $K_{r,s_1,\dots,s_j,t}$ when all $s_i$'s either equal 4 or are large enough and satisfy an extra condition. We also show lower and upper bounds for the non-induced problem in the case when $P$ is the complete three-level poset $K_{r,s,t}$. These bounds determine the asymptotics of $La(n,K_{r,s,t})$ for some values of $s$ independently of the values of $r$ and $t$.

Continuous Quantitative Monitoring of Mural, Platelet-Dependent, Thrombus Kinetics in the Crushed Rat Femoral Vein

1991 ◽  
Vol 65 (04) ◽  
pp. 425-431 ◽  
Author(s):  
F Stockmans ◽  
H Deckmyn ◽  
J Gruwez ◽  
J Vermylen ◽  
R Acland
Keyword(s):  
Thrombus Formation ◽  
Femoral Vein ◽  
Maximum Size ◽  
Digital Analysis ◽  
Video Recordings ◽  
Quantitative Monitoring ◽  
Set Up ◽  
Kinetics Of ◽  
Quantitative Nature

SummaryA new in vivo method to study the size and dynamics of a growing mural thrombus was set up in the rat femoral vein. The method uses a standardized crush injury to induce a thrombus, and a newly developed transilluminator combined with digital analysis of video recordings. Thrombi in this model formed rapidly, reaching a maximum size 391 ± 35 sec following injury, after which they degraded with a half-life of 197 ± 31 sec. Histological examination indicated that the thrombi consisted mainly of platelets. The quantitative nature of the transillumination technique was demonstrated by simultaneous measurement of the incorporation of 111In labeled platelets into the thrombus. Thrombus formation, studied at 30 min interval in both femoral veins, showed satisfactory reproducibility overall and within a given animalWith this method we were able to induce a thrombus using a clinically relevant injury and to monitor continuously and reproducibly the kinetics of thrombus formation in a vessel of clinically and surgically relevant size

Persistence of giants: population dynamics of the limpet Scutellastra laticostata on rocky shores in Western Australia

2020 ◽  
Vol 646 ◽  
pp. 79-92
Author(s):  
RE Scheibling ◽  
R Black
Keyword(s):  
Population Dynamics ◽  
Western Australia ◽  
Size Structure ◽  
Survival Rates ◽  
Maximum Size ◽  
High Rate ◽  
Adult Survival ◽  
Rocky Shores ◽  
Adult Size ◽  
Decadal Time Scale

Population dynamics and life history traits of the ‘giant’ limpet Scutellastra laticostata on intertidal limestone platforms at Rottnest Island, Western Australia, were recorded by interannual (January/February) monitoring of limpet density and size structure, and relocation of marked individuals, at 3 locations over periods of 13-16 yr between 1993 and 2020. Limpet densities ranged from 4 to 9 ind. m-2 on wave-swept seaward margins of platforms at 2 locations and on a rocky notch at the landward margin of the platform at a third. Juvenile recruits (25-55 mm shell length) were present each year, usually at low densities (<1 m-2), but localized pulses of recruitment occurred in some years. Annual survival rates of marked limpets varied among sites and cohorts, ranging from 0.42 yr-1 at the notch to 0.79 and 0.87 yr-1 on the platforms. A mass mortality of limpets on the platforms occurred in 2003, likely mediated by thermal stress during daytime low tides, coincident with high air temperatures and calm seas. Juveniles grew rapidly to adult size within 2 yr. Asymptotic size (L∞, von Bertalanffy growth model) ranged from 89 to 97 mm, and maximum size from 100 to 113 mm, on platforms. Growth rate and maximum size were lower on the notch. Our empirical observations and simulation models suggest that these populations are relatively stable on a decadal time scale. The frequency and magnitude of recruitment pulses and high rate of adult survival provide considerable inertia, enabling persistence of these populations in the face of sporadic climatic extremes.

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